基于局部平均采样的多维随机场景重构原理与方法

项目名称： 基于局部平均采样的多维随机场景重构原理与方法

项目编号： No.60872161

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 数理科学和化学

项目作者： 宋占杰

作者单位： 天津大学

项目金额： 28万元

中文摘要： 信息论之父香农（Shannon C. E.）在1949年提出任何能量有限的信号可以由采样值完全重构，采样频率与信号的Fourier变换的支集有关, 从而引起了信号处理领域的一场革命。但是在实际处理中, 由于测量仪器的惯性或信号逼近空间的要求, 所得到的采样值并不是时间变量在该点的精确值, 而是该点附近的局部平均值。本项目主要是在宋占杰的博士论文《随机信号的局部平均采样》的基础上，研究多维确定性信号局部平均采样的逼近阶、截断误差估计；研究多维随机过程在局部平均意义下的均方误差估计、截断误差估计、小波框架重构稳定性，以及以概率1收敛的相应结果。应用方面主要研究基于雷达信号局部平均采样的波浪反演重构算法以及基于天津市某区域水井的电测井局部平均采样数据，进行预处理和分析，重构天津市该区域地下水分布结构。在此基础上进一步研究统一的基于局部平均采样的多维随机场景重构的基本数学模型、原理与方法。

中文关键词： 重构；香农采样定理；局部平均采样；随机场景

英文摘要： The sampling theorem introduced by C. E. Shannon in 1948, who is the father of information theory. This theorem caused a revolution in the field of signal processing. Its basic idea is presenting any signals which energy is finite can be reconstructed by a sequence of discrete samples，the sampling rate is connected with the supported set of the Fourier transform of the signal. But due to physical reasons, e.g., the inertia of the measurement apparatus, measured sampled values obtained in practice may not be values of the original signal at the sampling points precisely, but only local averages of the signal near the sampling points. We will extend the results of Song Zhanjie's Ph. D. thesis- the theorem of random signals by local averages, and give the results on degree of approximation and truncation error estimate on multidimensional deterministic signals by sampling of local averages, and discuss the mean square error, the truncation error estimate, the stability of reconstruction by wavelet frame, the convergence with probability 1 on multidimensional random signals by sampling of local averages. About its applications, we will give the reconfiguration algorithm on the inversion of ocean wave by radar signals on sampling of local averages, process and analysis the data of electric logging well on sampling of local averages about some region in Tianjin , reconstruct the distribution of ground water on the region in Tianjin, give the mathematical model, the principle and methods of multidimensional random scence reconstruction on sampling of local averages.

英文关键词： recomstruction; Shannon Sampling Theorm; local average sampling; random scence